{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from IPython.core.pylabtools import figsize\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.rcParams['savefig.dpi'] = 300\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "figsize(12.5, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "colors = [\"#348ABD\", \"#A60628\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 不同lambda取值下泊松分布的概率质量函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Probability mass function of a poisson random variable,        differing \\\\$\\\\lambda$ values')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.arange(16)\n",
    "poi = stats.poisson\n",
    "lambda_ = [1.5, 4.25]\n",
    "\n",
    "plt.bar(a, poi.pmf(a, lambda_[0]), color=colors[0],\n",
    "                  label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n",
    "                  edgecolor=colors[0], lw=\"3\")\n",
    "\n",
    "plt.bar(a, poi.pmf(a, lambda_[1]), color=colors[1],\n",
    "                  label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n",
    "                  edgecolor=colors[1], lw=\"3\")\n",
    "\n",
    "plt.xticks(a + 0.4, a)\n",
    "plt.legend()\n",
    "plt.ylabel(\"Probability of $k$\")\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.title(\"Probability mass function of a poisson random variable,\\\n",
    "        differing \\$\\lambda$ values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 不同lambda取值下指数分布的概率密度函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.linspace(0, 4, 100)\n",
    "expo = stats.expon\n",
    "lambda_ = [0.5, 1]\n",
    "\n",
    "for l, c in zip(lambda_, colors):\n",
    "    plt.plot(a, expo.pdf(a, scale=1./l), lw=3,\n",
    "             color=c, label=\"$\\lambda = %.1f$\" % l)\n",
    "    plt.fill_between(a, expo.pdf(a, scale=1./l), color=c, alpha=.33)\n",
    "\n",
    "plt.legend()\n",
    "plt.ylabel(\"PDF at $z$\")\n",
    "plt.xlabel(\"$z$\")\n",
    "plt.ylim(0,1.2)\n",
    "plt.title(\"Probability density function of an Exponential random variable;\\\n",
    " differing $\\lambda$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 加载待分析的短信息数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x1050 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3.5)\n",
    "count_data = np.loadtxt(\"data/txtdata.csv\")\n",
    "n_count_data = len(count_data)\n",
    "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n",
    "plt.xlabel(\"Time (days)\")\n",
    "plt.ylabel(\"count of text-msgs received\")\n",
    "plt.title(\"Did the user's texting habits change over time?\")\n",
    "plt.xlim(0, n_count_data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 用PyMC3分析短信行为"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "import theano.tensor as tt\n",
    "\n",
    "with pm.Model() as model:\n",
    "    alpha = 1.0/count_data.mean()  # Recall count_data is the\n",
    "                                   # variable that holds our txt counts\n",
    "    lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n",
    "    lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n",
    "    \n",
    "    tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    idx = np.arange(n_count_data) # Index\n",
    "    lambda_ = pm.math.switch(tau >= idx, lambda_1, lambda_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    observation = pm.Poisson(\"obs\", lambda_, observed=count_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/pytorch/lib/python3.6/site-packages/pymc3/sampling.py:468: FutureWarning: In an upcoming release, pm.sample will return an `arviz.InferenceData` object instead of a `MultiTrace` by default. You can pass return_inferencedata=True or return_inferencedata=False to be safe and silence this warning.\n",
      "  FutureWarning,\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "CompoundStep\n",
      ">Metropolis: [tau]\n",
      ">Metropolis: [lambda_2]\n",
      ">Metropolis: [lambda_1]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='60000' class='' max='60000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [60000/60000 00:11<00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 5_000 tune and 10_000 draw iterations (20_000 + 40_000 draws total) took 12 seconds.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "### Mysterious code to be explained in Chapter 3.\n",
    "with model:\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(10000, tune=5000,step=step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_1_samples = trace['lambda_1']\n",
    "lambda_2_samples = trace['lambda_2']\n",
    "tau_samples = trace['tau']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x3000 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 10)\n",
    "#histogram of the samples:\n",
    "\n",
    "ax = plt.subplot(311)\n",
    "ax.set_autoscaley_on(False)\n",
    "\n",
    "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
    "         label=\"posterior of $\\lambda_1$\", color=\"#A60628\", density=True)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.title(r\"\"\"Posterior distributions of the variables\n",
    "    $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n",
    "plt.xlim([15, 30])\n",
    "plt.xlabel(\"$\\lambda_1$ value\")\n",
    "\n",
    "ax = plt.subplot(312)\n",
    "ax.set_autoscaley_on(False)\n",
    "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
    "         label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", density=True)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlim([15, 30])\n",
    "plt.xlabel(\"$\\lambda_2$ value\")\n",
    "\n",
    "plt.subplot(313)\n",
    "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n",
    "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n",
    "         label=r\"posterior of $\\tau$\",\n",
    "         color=\"#467821\", weights=w, rwidth=2.)\n",
    "plt.xticks(np.arange(n_count_data))\n",
    "\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.ylim([0, .75])\n",
    "plt.xlim([35, len(count_data)-20])\n",
    "plt.xlabel(r\"$\\tau$ (in days)\")\n",
    "plt.ylabel(\"probability\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3750x1500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 5)\n",
    "# tau_samples, lambda_1_samples, lambda_2_samples contain\n",
    "# N samples from the corresponding posterior distribution\n",
    "N = tau_samples.shape[0]\n",
    "expected_texts_per_day = np.zeros(n_count_data)\n",
    "for day in range(0, n_count_data):\n",
    "    # ix is a bool index of all tau samples corresponding to\n",
    "    # the switchpoint occurring prior to value of 'day'\n",
    "    ix = day < tau_samples\n",
    "    # Each posterior sample corresponds to a value for tau.\n",
    "    # for each day, that value of tau indicates whether we're \"before\"\n",
    "    # (in the lambda1 \"regime\") or\n",
    "    #  \"after\" (in the lambda2 \"regime\") the switchpoint.\n",
    "    # by taking the posterior sample of lambda1/2 accordingly, we can average\n",
    "    # over all samples to get an expected value for lambda on that day.\n",
    "    # As explained, the \"message count\" random variable is Poisson distributed,\n",
    "    # and therefore lambda (the poisson parameter) is the expected value of\n",
    "    # \"message count\".\n",
    "    expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n",
    "                                   + lambda_2_samples[~ix].sum()) / N\n",
    "\n",
    "\n",
    "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n",
    "         label=\"expected number of text-messages received\")\n",
    "plt.xlim(0, n_count_data)\n",
    "plt.xlabel(\"Day\")\n",
    "plt.ylabel(\"Expected # text-messages\")\n",
    "plt.title(\"Expected number of text-messages received\")\n",
    "plt.ylim(0, 60)\n",
    "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n",
    "        label=\"observed texts per day\")\n",
    "\n",
    "plt.legend(loc=\"upper left\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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